Aviation Tax

Once upon a time I had a math teacher, an old school, male, teacher who taught geometry as though the ability to bisect an angle with a compass was going to be a life skill that could sustain us in our old age. I'm pretty sure I could still bisect an angle if my life depended on it but then angle bisection is the sort of thing you'd figure out how to do pretty quickly on your own, so long as for you messing around with a compass was about drawing arcs and not seeing how many different things you could stab holes in with the pointy end. The latter seems to me a more life sustaining skill than bisecting angles, but I don't have a bad word to say about geometry.

My math teacher cared about his students, even sponsored a shiny award plaque for the top math student in grade eight. And he would encourage us to get going in life. I suppose math was a frequently failed subject. He'd urge us to do well, and if we couldn't do well right away, to go to summer school and get the course completed. He was very fond of telling us that if you spend one more year in school than you need to, you will lose one year of the top salary you will earn in your life. Students often looked confused when he said this. He thought we couldn't understand that we weren't losing the first year of pay, because they were going to get that anyway, that the money was going to come off the top end, right before retirement.

I'm not sure if he realized that we were confused by the unstated assumption. We didn't see our future careers as an even steady staircase leading upwards in salary from fresh out of school to the day we would retire at sixty-five. Do people do that? It was only two years ago that I reattained the salary of my first career, the one that I left to go into aviation. Given that money was probably worth a bit more back then, I may not have reached that level yet. There are other careers with published salary schedules that I could step sideways into with a slight salary decrease, and then pass my current salary quite quickly, for a bigger pile of money on retirement. But I don't think I'll make the career change. I like flying.

And that's how it works. There are some captains at the major airlines that make a metric tonne of money, but for the most part people in aviation make less money than people with comparable training, experience and responsibility do in other fields. The people who maintain my airplane make less than the ones who maintain my car. The people who taught me to fly made less than the ones who taught me to drive. It goes all the way up: there's never a shortage of investors willing to lose money on aviation. Aviation is cool. That's the tax.

Oxygen Exchange

I work in an unpressurized aircraft at altitudes where the atmospheric pressure is low enough that oxygen is required. Between 10,000' and F180 (about 18,000') I wear a nasal cannula: an arrangement of tubes, including two blowing oxygen up my up my nostrils. Above FL180 I wear a mask that covers my nose and mouth. I could skip the cannula and wear the mask any time I was above 10,000' but I can't eat or drink while wearing it, so it gets old fast. Plus the design of the cannula is such that it recycles exhaled oxygen, meaning that the oxygen supply lasts a lot longer on cannulas. Thus we only use the masks if we're working above 18,000'.

Putting the mask on involves taking off my headset, putting the mask over my face, pulling the head strap into place, putting the headset back on, and fastening another mask strap behind my neck. Finally I have to swap the microphone plug for the headset boom mike with the microphone plug for the in-mask mic. I can do all this before take-off, which I will if I'm in busy airspace. I started up next to a military jet once and noticed its pilot put on his oxygen mask before start up. If I am in uncontrolled airspace, I typically put my mask on just before I climb through 10,000'. If I'm expected to be monitoring a frequency, I wait until a needy or slow-talking pilot starts to make a call irrelevant to me, and then I can get the headset off, mask on, and headset back on before the call is over, ensuring I don't miss any calls. It takes less than thirty seconds. On descent, I can use the same technique, or just leave it on until I park, likely confusing the FBO marshallers.

Sometimes the day starts out with an hour of work at at 20,000' and then progresses to three more at 15,000'. Obviously I need the mask for the high level work, but would prefer to be able to eat and drink for the rest of the flight. In this case the swap involves all of the above, plus disconnecting the mask from the oxygen receptacle, connecting the cannula, and putting the cannula in my nostrils. It looks just like the cannulas the patients in House wear, but rather than looping around my ears and hanging down in front, it just goes around my head, held up by my headset earcups, and secured in place with a baseball cap. The point of this post is that I think about perfecting the swap between oxygen supplies at altitude. Should I breathe normally, or hold my breath during the swap?

The way breathing works is that the partial pressure in the air I inhale is greater than that in the lung capillaries it is in contact with. The imbalance causes oxygen to diffuse into the capillary, until the partial pressures are equal, the way any gas does across any membrane. So if the partial pressure in the ambient air is less than that of my lung capillaries, the act of breathing will actually decrease the oxygen level in my blood, and it would be better to hold my breath while I switch between mask and cannula.

The partial pressure of oxygen in ambient air at sea level is 21% of 29.92 inches of mercury, which is 6.28 inches of mercury. I'm going to convert that 160 mm Hg, not because I'm obsessed with metric, but because Wikipedia gives me biological numbers in millimetres of mercury so I have to convert one of them in order to do the math. At 18,000' the partial pressure of oxygen in the ambient air is half that at sea level, so 80 mm Hg. The partial pressure of oxygen in lung capillaries at sea level is 20-40 mm Hg, and as the mask maintains my blood oxygen at the same saturation as at sea level, then that's the partial pressure of oxygen while I'm wearing an oxygen mask. Eighty is clearly greater than forty, so even at 18,000' breathing is better than holding my breath to maximize blood oxygen during the mask swap.

So at what altitude should I hold my breath? At 32,800' the partial pressure of oxygen in the atmosphere is 25% of the sea level pressure, which is 40 mm Hg, the top of the range for lung capillary pressure. I would say, "so up to 32,000 it's better to breathe than hold one's breath when swapping oxygen sources" but above 32,000' the time of useful consciousness without oxygen is around a minute, even with no physical activity, so one shouldn't be messing around with one's oxygen source at such altitudes. But my conclusion is that above that, hold your breath for those few seconds of scrabbling before you either get your oxygen on or forget how and pass out.

I only took biology to about grade eight, so most of what I know about the human cardiovascular system comes from lifeguard class. I welcome any corrections to this analysis, even if you're stopping by years after I wrote it.

I See Fourteen Lights

There might be fog or mist present when I depart tomorrow from an uncontrolled aerodrome. The minimum allowable visibility for my departure is half a statute mile, so I need to be able to determine how far I can see along the runway, without a tower, a flight service specialist or an electronic runway visual range (RVR) measurement. I'll have to count runway lights.

I haven't done this in a while--you don't get fog much in the summer--so I had to double check some numbers. I found then in A Quick Reference: Airfield Standards from the US FAA. (Nice little reference. I intend to read it through in its entirety sometime, maybe while waiting for fog). It confirms for me that the lights along the runway edge are spaced 200' apart. There are six thousand feet in a nautical mile, but for some reason ground visibility is measured in statute miles, which contain only 5280 feet apiece. (I had to look that number up, too). That means that I need to be able to see half of that, or 2640' feet along the runway to meet the half-mile minimum visibility. And at this point I realize "well duh: if there is an RVR then a half mile is RVR 2600." So I'm on track. This means that if I pull onto the runway even with one set of runway lights (they are aligned with each other on each edge of the runway) I need to be able to count 2600 divided by 200, or thirteen more pairs of them, stretching away into the foggy gloom, in order to be legal. I'm happy to ignore the extra 40' because RVR values do, and because I'm looking along the hypotenuse of the triangle whose base is on the runway edge, and surely I'll pick up another forty feet there.

Whom am I kidding? This is Cockpit Conversation. We don't make assumptions about trigonometry here, we do trigonometry. The base of the triangle runs from my position at the first runway edge light, to the fourteenth runway light, and is 2600' long. Assume I'm in the middle of a runway, standard width 200', making the height of the triangle 100'. The measurement of the hypotenuse is therefore sqrt((2600 x 2600)+(100 x 100)) = 2602. So no, actually, there is almost no difference between the distance from the first runway light to the fourteenth, and the distance from my eye to the fourteenth light. That's a very skinny triangle. My assumption is wrong. So if I wanted to be a nerd, I could park thirty-eight feet back from the first pair of runway lights. But generally I want to go flying.

In order to save Americans time telling me that the RVR for half a mile is 2400, I'll confirm that in Canada and the other countries I checked researching this post, the RVR for half a mile is 2600. I don't know why Americans use 2400, and neither do the people in this thread on the subject. I especially like the way that the person who initially answers the question there doesn't notice that RVR 2400 for a half mile doesn't add up, until the student points it out. Another thing I expect American commenters to want to tell me today is that "if you have to count runway lights on short final, you should go missed." That's becase their landings are legally restricted by visibility. But Canadian landings are governed only by decision height or MDA. If the runway is visible at DH/MDA, a landing is authorized for us. Our plates have an "advisory visibility" which we can use to calculate whether we expect to be visual at minimums, but its value does not affect our legality to put the airplane on the runway. Once we are past the FAF, the RVR does not restrict us. We do have something called an approach ban which can stop us from legally attempting an approach in terrible visibility, but that's a whole 'nother topic.

Guilty Little Pleasure

I love conspiracy theories. I love the idea that the facts as presented could be explained in a way that fits the just as well as the accepted explanation, especially when it conveniently explains some other facts that are conventionally held to be unrelated, but mysterious. So for me "we didn't actually land on the moon: they faked it in a studio" doesn't qualify as fun, because "I don't understand physics well enough to understand how space travel works" isn't a fact that I need explained. But some things do need explaining. We complain when a movie or a book leaves loose ends, and we expect our stories to wrap everything up. If there's a gun in act one, someone needs to be shot by act three. If a loquacious limo driver dominates the prologue, he has to have a role in the denouement. And if an airliner disappears without a verifiable trace, and then another airliner that looks almost the same drops out of the sky in a war zone, we demand that the two be related.

As you may recall, the incomplete location data from MH370 suggested that the airplane was somewhere on a line stretching from Kazakhstan to Australia. My favourite conspiracy theory (link in Russian) postulates that MH17, shot down on the Ukrainian/Russian border, is the same aircraft. MH370, the theory goes, ended up at an American military base Diego-Garcia. from there the CIA transported it to the Netherlands where it took off packed with explosives and the already dead bodies of the original passengers. The pilots parachuted out and the airplane continued on autopilot to the designated location, where it was programmed to explode.

"Evidence" presented for the theory includes the undocumented claims that:

• passports found at the site were all very new, and unscorched
• some of the passports were clipped or punched in the way that their countries indicate invalidated passports
• a flight status screen showed the flight as cancelled
• the registration of the two aircraft differs only by an O versus a D: 9M-MRO for MH370 and 9M-MRD for MH17
• no relatives gave media interviews
• all the Facebook accounts of the passengers were created on April 21st, after the disappearance of MH370, and nothing was posted to them
• The configuration of windows and painted flag shown on news photos of the wreckage matches MRO, not MRD.
• the corpses were said to have a strange odour, and seemed to be drained of blood, not freshly dead

Now I don't have a problem with passports being found in excellent condition despite being onboard an airplane that was shot down. The passports were not in the engines nor the fuel tanks. They were probably in protective cases in secure pockets of people's carry-ons, at least that's where mine is. Unlike human beings, passports held flat the way people tend to put them away are not damaged by extreme pressure changes or long falls, and if we trust Ray Bradbury can sustain temperatures approaching 451 Fahrenheit.

The clipped passports thing is a little odd. I suppose there may be people who keep their expired passport with their valid one. I've seen pilots produce multiple licences ... actually I remember doing that myself once at a flight test. I'd just added the new paper to the original. The examiner told me to put the old one away at home somewhere. Now I have a file folder full.

I'm not surprised that the flight information site would mark the flight cancelled, seeing as they almost certainly didn't program it with the option of "shot down by missile". The data at that page--the same flight number on consecutive days--could be interpreted as a record of arrivals, and the arrival of the July 14th flight has most decidedly been cancelled.

The similarity in the registrations is kind of startling, and it is actually true. It would be a good way to cast doubt on a report by someone who claimed to have seen a change in the tail number from departure to arrival, but it becomes a lot less mysterious if you consider that all Malaysian Airlines operates B777s registered as 9M-MRA through to 9M-MRQ. The prefix 9M simply represents Malaysia, and it's very normal for an airline to buy several aircraft at once and have consecutive registrations.

Perhaps relatives in other countries were more circumspect, but the distraught sister of Andre Anghel, the lone Canadian on board, allowed herself to be interviewed on the radio. I had to pull over and cry after listening to her. She spoke about her brother going to medical school in Romania and then on holiday with his German girlfriend. She had sent him a text saying she loved him, and it was very important to her that he had seen that text before he turned his phone off for the last time, but she didn't know if he had.

Andre has a Facebook page, created January 21st 2007, and the good sense to keep most of his posts private, but updates to his public profile picture, along with comments on them from his friends can be seen prior to the disappearance of MH370.

I like the windows one, because it makes plane spotters into sleuthing heroes, the holders and creators of a distributed database of information on these airplanes that is also shared with the world through sites like airliners.net. I'll leave it to someone else to resolve the disappearing window mystery.

Here are some more English language sources for these and other bizarre conspiracy theories about the two flights. I like the one that just says matter of factly that aliens were responsible for MH370, now let's move on to MH17.

My theory, and it's a pop psychology theory, not a conspiracy theory, is that in this big confusing world, it's on some level comforting that someone has everything under control. Some people prefer to believe that their own government would kill thousands of people, largely their own citizens, as a calculated provocation, than accept that that same government, tasked with their protection, would fail to act against foreign terrorists. Planes don't get accidentally shot down or disappear for no reason we can know. It's all linked up and someone is in control. It's like when you're a kid and trusting that your parents really do know everything. It's like believing that when things go wrong it's a test, it's making way for something better to happen. Anything other than the possibility that things just happen. People abhor disorder and terrible things that have no explanation. Religions literally arise from such things.

Also if you speak a language you want to practise, read things that interest you. My new word of the day is якобы supposedly, a word no Russian-speaking conspiracy theorist should be without.

Solve for X

Today someone in an aviation workplace was either amused or insulted, I'm not sure which, by my excitement that he was genuinely using trigonometry for real things. I'm afraid that he may have thought that my excitement and admiration was over the fact that he knew how use trigonometry at all, but really this is just one cool part of a very cool project he is working on.

What do you think he's up to?

The Winners Are ...

And now, after much legitimate waiting because I was busy and just a bit of deliberate tantalizing because it's fun, are the results of the Nosewheel Roulette game.

Here is the nosewheel during my preflight inspection, on the ground at an airport expereinced readers may recognize. I actually marked the nosewheel the night before, after parking, in case I was in a hurry the next day, because I had been that day and forgot to do it on the first appropriate flight. Yes, that may not be exactly at bottom dead centre. I had intended to use a plumb bob, but the wind was howling, so that wouldn't have done any good, and I didn't bring a spirit level.

Here is the nosewheel after flight, parked in almost the same place, as we returned to the departure airport that day. It's actually both before and after fuelling, because there was an airplane parked at the avgas pumps when I arrived. I contemplated parking behind it, but that would have blocked the Jet pump, and a helicopter might have needed fuel while I was waiting. So without shutting down I taxied from the runway, to the pumps, to parking, then did a little indecisive twirl, then finally shut down where you see it.

I couldn't find my tailor's tape, the cloth measuring tape I originally used to determine the circumference, but as you can see the mark ended up fairly close to all the way around, and the wind was blowing even harder than the day before, which kept tearing the masking tape I was going to use as an intermediate, so I measured backwards from the bottom and then subtracted that from 128 to find the winning number. I measured two ways, once by cutting a piece of masking tape the right length, intending to save it until I found a ruler, but then I remembered there was a measuring scale on the edge of the chart magnifier I keep on my clipboard. I measured the masking tape with that, then used the flexible measuring tape to measure the distance directly, and both came up with ten centimetres, giving a final position of 118 cm clockwise from the bottom.

(In answer to the valid question on the original post, regarding why clockwise around the left side of the wheel: because that's what first occurred to me. I approach the airplane from the left, like it was a horse, so it doesn't get spooked, I guess, and clockwise seems like the normal way to go. True, it's not the direction the wheel rolls, but I didn't think that closely about it before making the rules).

Speaking of rules, I decided not to disqualify anyone for not following them, except that people who didn't post a guess in the comments didn't get entered at all. You'd be astonished by the number of ways people managed to not follow the instruction: "Post your selection in the comments, then back it up with an e-mail to me with the subject Sunglasses." Another time I may automate the process, so be warned. Here are your winners.

Nosewheel Roulette Spreadsheet

I have completed the nosewheel roulette flight and computed the results, but just to keep things both geeky and suspenseful around here, I will first present my computations for debugging and critique.

I filled a spreadsheet (Open Office - I told you we were going to be geeky) column (column A) with the numbers 0 to 128. (Yes, the numbers should only go to 127, but someone picked 128. Because a wheel is round, that wraps him back to zero, but I didn't put him in the zero box because it was a test of my algorithm having it there).

In the next column (B) of the spreadsheet I put an x next to all the numbers that were spoken for by someone, based on the posted comments. In the next column I put something else I ended up ignoring and in the final column (D), I calculated the distance each guess was from the actual by taking the lesser of:
- the difference between the guess and the answer
AND
- 128 minus the difference between the guess and the answer.

In other words, I measured the shorter distance around the wheel between your guess and the actual final position. If the difference between your guess and the answer was greater than 64, you're getting closer to the answer round the other way.

In the spreadsheet this formula was:
=IF(B4="x";MIN(ABS(F$3-A4);128-(ABS(F$3-A4))))
(There's probably a neater way to do that with modular arithmetic, but I was watching TV at the time and my brain kept resetting).

In the formula, B is the column that has an x to indicate that the number is spoken for, F$3 is the measured answer, and A4 is the guess in row 4. I copied this formula down the whole column (the spreadshhet automatically increments A4 for each row). And then finally I sorted the spreadsheet row-by-row on value in column D, the result of that formula.

I'll leave this overnight for you to find any glaring errors or controversies, before I present the results, your SunglassesShop.com sunglasses winners, and the booby towel designee.

Illogical Hope

I'm still holding out faint hope for the employer that never called back. The first aviation job I ever got was offered to me after the "expect a call by" date. Sometimes it takes longer than an employer anticipates to make a decision. Maybe I'm not their first choice, but they don't want to tell me to foad yet, because the first choice candidates might go to Air Canada before they get on there. I left a polite "could you please let me know if all the successful candidates have been notified" message on the chief pilot's voicemail, and I'm a little surprised that they didn't at least e-mail, because they seemed to be more respectful than that.

I get home from grocery shopping and there's a phone message. Oooh, lovely phone message. I press the button. It's from a charity that wants to come and pick up used clothing, furniture and small appliance donations. Hey, disabled people, if I get that job you can have bags of it, as I move across the country again. I realize what I've been doing wrong though. I bought a little electric grinder, for grinding spices, because they taste so much better fresh, and I decided I wouldn't open it until I got the job and moved to the new town. That's not how superstition works! I have to open the box, throw the packaging away, and then I will get the job and have to pack it up and get cinnamon or cumin all over my towels. I take it out and use it.

I found this story (many of you have probably already seen it on Bruce Schneier's blog) interesting twice. First, there's the idea that the logic of "If P then Q; P. therefore Q" or "If P then Q; Not Q. Therefore not P," is difficult. I really didn't know that most people found it difficult to follow.

When I was in university there was a third year philosophy course that math majors took for an easy arts credit. (I never grasped the concept of paying for useless courses, so I didn't take it, but I trust the accounts of my friends). It was trivial logic problems. All you had to do was memorize the names of the different types of actual logic and logical fallacies and it was an easy A. You didn't even have to attend the classes. I guess I hang out with logical people. Perhaps I should have followed the logic that if they could get As without trying, there must be other people who were getting the marks at the other end of the scale, but then we also laughed at the kinesiology students whose hardest course was a special version of first year physics that allowed them to understand skeletal structure and musculature in terms of basic Newtonian physics of levers, mass and energy.

I imagine most of my readers will also find that type of logic simple, because the logical elite hang out with me. but I'm fascinated that even those of you who would fail the "if someone is going to Boston he takes a plane" card-flipping test nevertheless have no trouble with the exact same logic in the "has to eat vegetables to get dessert" card test. And I'm now mature enough to realize that people have different skills, and if I hurt my abductor hallucis (which I think I may have) I'd be better off consulting a kin grad than a mathematician.

In case you're wondering, there's no connection between my waiting for an employer to respond and taking a plane to Boston, eating dessert, hurting my foot, or minding my logical Ps and Qs. They're just the top things on my pile.

Charter Planning

I'm planning a passenger charter in the airplane with the irritating weight and balance. It can't be flown single pilot with full fuel, so when a charter involves something like flying to A to get people, dropping some off in B, picking more up in C, and taking them all back to A, you have to plan ahead carefully to make sure each leg will work for the number of people and the seats you have put in the plane.

Every fleet seems to have one of these: an airplane that is the same type as the others but through some quirk of history and equipment is way out of balance. I wonder if this continues to widebodies and there's some United captain today looking at his loadsheet and saying to his FO, "Great. We've got N124SA today." Does Air Canada have one B767 that dispatchers and loadmasters despise, and long to see get a shiny new paint job and be towed by the new girl on the ramp crew or left outside in a hurricane? (It's always the shiniest airplane in the fleet, or the one featured in advertising, which gets destroyed in a freak accident).

I work out the permutations and then that airplane is grounded for some mysterious engine problem unrelated to the weight and balance.

A Change is as Good as a Rest

Pretty much the minute I get home from work, I'm asked for help ferrying an airplane. (That's because I check my e-mail the minute I get home from work, but don't you?) This one isn't a job, it's a freebie for the woman who brought me to Oshkosh a couple of years ago on flight passes. She has the use of a tiny little airplane, a Cessna 150, and her employer has suddenly transferred her across the country, so she wants to move the airplane from an airport near Toronto to one near Vancouver. She has a commercial licence, but not a lot of experience, and wants a companion for the trip. As soon as I've done my laundry and repacked I'm back on the road.

The parameters of the trip are that we don't take off unless we're assured of being able to land at an airport in the Air Canada system, including Air Canada Jazz, so we can get home, and we don't fly in snow or heavy rain. She's PIC because the insurance is in her name, and she's not happy flying in those conditions. Of course the weather has to be VFR, because it's a Cessna 150 with no navigation instruments. Not even an ADF. I caution her that we might not get the weather, but as airfare is not an issue, it's worth the trip even if we only get to Thunder Bay, so we go.

Toronto is on the north shore of Lake Ontario, on a peninsula between Lakes Ontario, Erie, and Huron. If you look at a map, Huron looks like a big lake with a smaller lake riding piggyback on it; Huron is almost divided in two by the Bruce Peninsula and Manitoulin Island. Just to the west of Huron is Superior, the largest freshwater lake in the world. The Great Lakes seem even bigger when you're in a tiny airplane. The northern shores of Huron and Superior are sparsely populated, and the airplane cruises at about 90 knots and only carries about 3.5 hours of fuel, so we have to plan the trip carefully. I'm not sure yet whether we're going to take the shortcut across Manitoulin Island or if we'll go the long way around by Sudbury. I need to get more information about weather conditions on the peninsula tomorrow.

The night before the trip we're in a hotel room in Brampton, Ontario. I deliberately brought absolutely minimal gear, not even my computer, because I thought after fuel our payload might be as little as 40 pounds. I still have to have clothes suitable for surviving overnight in the bush in Northern Ontario and clothing suitable for boarding Air Canada as a non-rev passenger. People riding for free have to pay their fare by looking good for the rest of you. I go through the aircraft documents and make sure they are all present. The weight and balance calculation is a pleasant surprise: with the two of us on board and full fuel we can still carry 91 pounds of gear. Skinny girls for the win! (I'm fairly certain I got my first flight instruction job through being a skinny girl, but I'm less sure whether that was for weight and balance or aesthetic reasons). Including our headsets, survival equipment, snacks and water and personal effects, plus the gear like spare oil, towbar, and tiedowns already in the airplane, I estimate that we'll be carrying more than eighty pounds. Things like that add up quickly. The weight and balance document is dated back in the 1970s, so I kind of suspect it isn't perfectly matched to the airplane we'll be flying, but if when you change out vacuum tubes for transistors the weight tends to go down not up, so I'm comfortable.

We sort out our baggage and a rough flight plan, hoping to get an early start. If all goes well we can reach Winnipeg in a day.

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Here's a new blog I found recently, Airline Pilot Chatter, it's airline pilot day in the life stories, infrequently updated but worth checking now and again. It gives the same sort of details that I do. I liked the story of ferrying an airplane to the graveyard.

Alidade

I mentioned the met station in Estevan. Once upon a time there was an FSS there, and a pilot could go up the stairs to get a weather briefing or look at weather charts, faxed from Edmonton, I think, and hand-coloured by the local briefers. Or you could phone the FSS directly to get the latest weather. You just had to be careful not to call them at the top of the hour, or else they would be outside taking the hourly weather observations, or busy coding the observation. About eight years ago they they separated the task of observer and briefer, moving the briefers into consolidated regional Flight Service Stations and leaving the lonely observers behind, in some cases literally building a solid wall across the door the pilots used to enter for briefings.

We first noticed the Nav Canada met observer when my passenger mistook him for a Transport Canada official--I guess he has a sharp eye for aviation functionaries. Late that day we spotted this device just outside the airport fence.

As you can see if you click and enlarge the photo, it consists of a ninety degree arc, fixed firmly to a vertical column and calibrated on a non-linear scale in "metres" and "coded vales." There is also a sight, pivoted so that it can swing through the arc. Its location, between the met office and the outdoor weather sensor array, plus the words Atmospheric Environment Service indicated that it had something to do with making weather observations, but what? The azimuth angle between the observer and the base of a randomly selected cloud is not a useful datum for a pilot, or for anything meteorological that I can imagine. I snapped a picture and saved it until now.

The observers at the airport where I learned to fly had a laser ceilometer, a device that bounces a short pulse of light off the cloud base and times its return. Speed times time equals distance, so you take the time it took to return and divide that by the speed of light and you have the distance the pulse travelled. Divide that by two (because it had to go there and back) and you have the height of the cloud above the emitter. I get a serious thrill out of the fact that a trivial calculation whose results I use daily involves the speed of light, so we must now pause for a big grin.

In mountainous areas, weather observers use the known height of nearby peaks to determine cloud heights by looking at where the cloud hits the mountains, but I hadn't until today given any thought to the pre-ceilometer technique in this notoriously non-mountainous province. (I made a two hour flight in Saskatchewan the other day and the elevation of the landing airport differed by one foot from my take-off point). The alidade and ceiling projector combination is the answer to the question I didn't think to ask.

The unfamiliar word alidade, describing the scale, looked eminently googleable so that's where I started. Technically the alidade is just the pointer with the sight, a part of many ancient and modern scientific instruments, but some whole instruments are called alidades by association. Fortunately for me this sort of alidade is one of the example pictures on Wikipedia, and links to the article on the ceiling projector with which it is used.

According to the Wikipedia article, the ceiling projector is a bright light that shines straight up at a known distance from and the same level as the alidade, and then the spot where the light reflects from the base of the cloud is observed with the alidade. The scale on the alidade is simply the solution to the resulting trigonometry problem. How beautiful is that? (If you won't at least pretend to appreciate the beauty of trigonometry you aren't allowed to read my blog anymore).

In my diagram, y is the height above ground of the alidade and the projector (relatively negligible for the ground-mounted instrument, but some of these are probably on rooftops), d is the distance between the alidade and projector, and A is the angle above horizontal of the observed light spot on the base of the cloud. You put your eye where the red dot is and raise the sight along the scale until the light spot lines up with both rings of the sight. The unknown x is the distance from the projector to the cloud base. Using trigonometric ratios, d tan A = x and then x + y gives you the cloud height above ground level. The scale is marked along the arc as the solution to the equation, instead of being in degrees, so the observer doesn't actually get the privilege of doing the math.

That's two ways to get the same information, one requiring knowledge of the speed of light and the ability to produce and monitor coherent nanosecond light pulses, and the other requiring only tools and skills known and available to ancients. If that's not the coolest thing you've seen all day then you are obligated to click on the comments and tell us all about your even cooler thing.

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For a scientific experiment of a different kind, there's Boobquake, a US college student's response to an Iranian cleric's assertion that earthquakes are caused by by women dressing immodestly. I'll join the effort and show some cleavage on Monday, provided that it's not snowing.

On Again

A new day, a new decision. We'll fly to Fairbanks, clear customs, and then take commercial flights home while maintenance does a phase check and the replacement crew flies in. Someone must have factored in the airfares and that shifted the math. Airfares are relatively cheap in and out of Fairbanks, as they are for most big-city American destinations. We won't get to see the remote Alaskan spot we had hoped to visit, but the novelty would probably have run out before the work, and we will get to cross northwest into Alaska.

After I get that news, I go flying. If all goes well, this will be our last flight returning to this base -- although my Alaska charts still haven't arrived. Apparently this place has some sort of repellent force that prevents newspapers, courier deliveries, mail and airline passengers from arriving on time.

The last three METARs report cloud bases at 5900', 5800', and 5700', which is odd because I asked the specialist earlier and he said they didn't have a ceilometer. All cloud heights are estimates. How would they, in the absence of nearby mountains, determine a hundred foot difference just by estimation? On other days the bases have been given to the nearest thousand feet. I ask about it.

The answer is that today, because the clouds are all cumulus, they are reporting the bases not by visual estimation, but according to a formula. I understand. I know that formula. I didn't know anyone used it for anything other than written pilot examinations. Here's how it works: cumulus clouds are formed when rising air is cooled to its dewpoint by expansion. Rising air cools through adiabatic expansion at a rate of 3 degrees Celsius per thousand feet. The dewpoint decreases by about 0.5 degrees per thousand feet. Therefore the temperature approaches the dewpoint at a rate of 2.5 degrees per thousand feet. The reported surface temperature is 21 degrees and the surface dewpoint is 5.2 degrees. So at the surface the temperature is 21 - 5.2 = 15.8 degrees above the dewpoint. The temperature will reach the dewpoint 15.8/2.5 = 6.3 thousand feet above the aerodrome. (This doesn't match the earlier report because they have given me current temperature and dewpoint values and the temperature-dewpoint spread has evidently increased by a degree since they did their last calculation. Drop the temperature to 20 and do the same math and you get 5900'). METAR altitudes are given above aerodrome elevation, which is 1250', so I can expect bases to be at about 7500' above sea level, as displayed on my altimeter.

Another pilot hearing this conversation calls in to report bases at 7500'. Science! It works. Also don't you love Canada? We have formulae that combine degrees C with Imperial feet and we think it's just fine that way.

In Canada either a flight plan or a flight itinerary must be filed for a VFR flight of more than 25 nm. A flight plan is filed with Nav Canada but a flight itinerary can be filed with anyone responsible enough to report you missing. Commercial operations like mine generally file with company and when we inform ATC of this we say we are "on a company note." That shortcuts ATC asking if we want them to open our flight plan. In imitation of this practice, a small aircraft pilot taxiing out calls the FSS and says he is "VFR to Helmut on a note." He then decides that this needs more explanation, as the FSS knows he is a private owner and not a company, so he adds, "My wife."

Another pilot calls up "Looking for the airways to Ft. St. John." That's a non-standard way to ask for an IFR clearance, but seeing as the FSS probably has his clearance sitting there and is is waiting for him to call to ask for it, he could probably have said anything he liked and still received it. If you don't ask for it, they offer it, as when the tower says to a airline pilot after he makes a taxi call. "Grab your pen."

Then it's my turn. The wind is straight down runway 26 at 10 knots, so it's an easy taxi and take-off. As the airplane waddles up to altitude in the hot weather I call to report airborne, and my turn. The FSS does a shift change. It's a woman with an unfamiliar voice, and she comments to someone on air that she's just back after two weeks. I guess she's out of practice, because she keeps getting confused, forgetting which airplane is where, scrambling our types and needing constant position reports. I am ready with a position report whenever she calls me for one and make sure I am keeping track myself of where the other aircraft are.

Refraction Distraction

I walk towards my airplane on the ramp and I can see that it is pissing fuel out of the left wing, a steady stream, not a drip but a spray like it's pressurized. I remember the wide-eyed horror I felt the first time I saw fuel streaming out of a parked airplane. Today my feeling is just, "Hmm, this had better not be something bad." I could write a long blog post on various reasons that fuel has dripped, flowed or sprayed out of my parked airplane. I duck under the wing to look at the source. It's coming out of a vent. The vent is recessed so that incident air doesn't pressurize it, but it still faces forward so the stream spurts out in front of the wing. There's no visible damage. To confirm my first suspicion about the cause, I open the fuel cap for that tank. The tank is completely full and some fuel flows out of the filler neck onto the top of the wing. Suspicion confirmed.

This airplane was fuelled last night while we were wearing sweaters and jackets on a rainy, overcast day. Now I'm wearing a t-shirt, and the angle of the sun over the hangar puts the left wing in bright sunlight. The fuel is expanding inside the wing and being forced out the vent. It's perfectly normal. That's one of the reasons the vent is there. (The other reason is so that as fuel is burned, air can get in to replace the volume so that the fuel will continue to flow).

The fuel stain on the ramp looks nasty, but the rest of the airplane is fine. I set up what gear I have, conscious that the bag in which I normally organize my spare batteries, extra flashlights, snacks, waterbottle, and the like is packed inside my checked luggage. I have enough equipment to be safe and legal, just not everything I usually have.

All is normal on the run up, and I talk to the flight services guy in the tower and then take off. I say good bye to flight services guy but continue to monitor his frequency, and tune 126.7 on the other radio for en route traffic. At eight-thirty in the evening up here the sun angle is like four in the afternoon down at the 49th. It's hot in the cockpit, but I need to run the heater for the comfort of the picky computer equipment in the back. I spend a while moving vent sliders around trying to make it comfortable for me, and cozy for the computers, too. The mission specialist goes off headset for a while in order to take off his fleece.

Not only have I not flown in three months, but they have changed out the type of equipment I am using, so I'm looking at a screen I haven't seen in about a year. I stare at it for a moment, trying to remember where it means I'm supposed to go, and then I go to work. I remember this. I know how to do it. I'm good at this. Somehow my temperament--and bladder--is suited for this type of flying. I settle back into my routine, burning an hour of fuel out of each set of tanks so that nothing is so full it's spilling out the vents, and then systematically work through the various tanks. I plan to land at 2:15 a.m.

There are a couple of pilots in Cessna 172s hopping around beneath me, position reporting between small places I saw on the map. They chat to each other about how fine the weather is tonight and where they are going. As they say their call letters I picture them painted on the side of the airplanes. I remember things better visually then as sounds. One of them is CXD, which trips a switch in my head because they are all letters used in Roman numerals: 110-500, not that that means anything. When there's a break in their conversation I call up CXD and ask them what they're doing, just trying to join the conversation. The answer is a fairly terse "flying from Worsely to Fairview." And then they stopped talking to each other. I guess they forgot they weren't alone up here.

Fifty gallons of avgas later I'm still in the sky and so is the sun. My hat is in my checked bag, so I have to depend on my skinny sunvisors and my sunglasses for protection from that ball of fire. I estimate it is still fifteen degrees above the horizon, maybe a little less. When will it set? When I'm flying I can't put my whole brain over to arithmetic, because I'm looking out the window, manipulating the controls, squinting at my screens, and paying attention to all the little things I don't even realize I'm looking at. So I chunk arithmetic up into easy bits. Three hundred sixty degrees in twenty-four hours, one hundred eighty in twelve, ninety in six, forty-five in three, so fifteen degrees an hour. But I know it will be in the sky for a lot longer than an hour. The sun doesn't go straight down here, it moves diagonally towards the horizon. At my latitude, three weeks before the solstice I suppose I could calculate its angle of descent and use trigonometry to determine when it will reach the horizon. But I just eyeball it and estimate that it will hit the horizon at about eleven. If I were a few degrees further north and it were a few weeks later it wouldn't go down at all. It would just slide around the edge of the horizon before angling back up.

I didn't see the exact moment it ducked behind the horizon, I just turned and saw that it was no longer trying to burn my eyeballs. It was about eleven. It's still light, but the light is more orangeish. I try to picture the refraction process that is making the light orange. I'm pretty sure it's the same reason that the sky is blue. But is it because the red light is refracted more by the atmosphere or less? I think the blue is refracted more, because the blue is on the inside of the rainbow, but I can't quite picture it. Now that I'm on the ground I could look it up, but I'll give you my airborne thought processes. I think that as the sun's rays hit the atmosphere at a low angle the blue is being refracted up away where I can't see it, but the red is refracted less, so it's the last colour I see. There's a moon, too, and its light is whiter. An hour after sunset it's not really dark yet. I can still see clouds in the distance and the shapes of lakes on the ground.

I call flight services for an altimeter setting. It hasn't changed in over four hours. 'Are you coming in to land now?" he asks. No, we have another couple of hours.

The mission specialist is tired and calls it done a little early. We touch down just before two a.m. I chat to the FSS guy on the way in, "when do you get to go home?" It turns out that he worked the day shift and then got called in to do the overnight, so he'll be there until 8:30 a.m. Nasty. I tell him he'll still be there when my flight partner comes on shift in a few hours. He asks her name so he can say hi. I forgot to ask his name.

I'm hungry enough to eat the seven hour old sandwich I bought before departure, and tired enough to go right to sleep.

Axioms of Thought

In Which Aviatrix falls so far into her own metaphors so as to no longer have room for the story she was trying to tell.

Sometimes I have discussions with people who don't seem to make sense. A lot of people have such discussions, which I think is why some people think liberals are stupid, some people think conservatives are ignorant, and why religion gets so much flak. It's far easier to assume that the person on the other side of the argument just doesn't get it, than to figure out the misunderstanding. I try to start with the assumption that the person is neither insane nor stupid, and go from there.

I had a months-long on-and-off internet argument with someone once. I thought it was a point of philosophy that I was begging him to compromise on for the sake of a project and he just kept throwing it back in my face, seemingly refusing to even acknowledge that there was a risk. That was finally resolved when we discovered two words crucial to the argument were synonyms to him, but had a vital contrast for me. Being that the argument was in text, his written English was near flawless, and the position he seemed to be taking was not uncommon, it took that long to track down the discrepancy. And this was an easy one, because it didn't really represent a difference in our underlying axioms.

By axioms I mean things that people believe or know in order to know or deduce anything else. Those of you with a mathematics background know that you can't have a system of knowledge without having some arbitrary ground rules first. Our mathematical system is based on axioms like things that are equal to the same thing are equal to one another. I mean duh!

The problem is, people often don't even know they have them. They build what may be a perfectly logical and coherent argument up from a base that the other person isn't standing on. It's like trying to get someone from an island over to your mainland by building a magnificent bridge between the mainland and completely different island. Here is where people start to think one another are insane morons. The islander says he can't drive over what the mainlander knows is an excellent bridge, so the mainlander decides it's all due to religious prejudice and gives up on islanders all together.

The nature of an axiom is that it is something so self-evident that it doesn't even need to be stated. So people assume that everyone accepts that axiom, or even when they know that some don't, they don't see that their logical arguments depend on it.

A common axiom of thought is that the world is God's divine creation and that He is omniscient and omnipotent. People for whom this is axiomatic can't prove it. They feel it, they know it, the enormity of creation demonstrates it. It is true because it is the original Truth. I need a short name for people who hold this to be a self-evident truth, and "creationist" won't do because believing in divine creation doesn't require belief that it happened in six days, six thousand years ago. I'll call them God-ists, because it's short. For the purpose of this discussion it carries no other meaning than "people for whom divine creation is a self-evident axiom," and I've made it up solely to abbreviate the phrase.

God-ists nowadays universally know that not everyone shares that belief, but it doesn't stop them from thinking arguments based on it should sway non-believers.

Don't think I'm being unfair to God-ists here. Their frequent adversaries, those whose axiom is that the universe is a completely logical place, entirely governed by forces that can be understood in a physical sense, often do not realize that that is an unprovable belief, an axiom that all their knowledge rests on. It is every bit as unprovable as the existence of an invisible pink unicorn. But many Sci-ists can't imagine someone being able to get through their daily life without seeing the self-evidence of this truth. They dismiss God-ists as deluded without it.

That's a simplistic presentation with lots of room to argue about. I only intended it as a familiar example. Many God-ists embrace the Sci-ist's axiom as a kind of Second Law of Godotics: "God set up the universe as a logical place, governed by physical forces, except for when He intervenes." That combination seems to be to be the closest fit to what we've observed, except that a Sci-ist states the identical observation as "The universe is a logical place, governed by physical forces, even when something happens that we don't yet know the physical explanation for." Just because once upon a time every sunset and sunrise was understandable only as an act of the gods and now we can understand the workings of cells and atoms doesn't mean that God didn't set it up that way, and just because we are unwinding more and more of the wrappings of our physical world doesn't mean that there isn't still something at the core that is not susceptible to physical laws.

Whew, this got way more theological than I intended. I wonder if that's the feeling of the theoretical physicists who end up writing books or participating in projects like What The Bleep Do We Know? when all they are doing is trying to understand chaos theory and the fundamental nature of energy and matter in a rigid scientific way. I think of science and religion both working on the same immense jigsaw puzzle, with science rigidly sorting out all the edge pieces and carefully fitting pieces one into the other, trying to build up in a consistent manner from the border to the inside, while religion plucks pieces out of the box and tries to fit them together without knowing or caring which way up they go or how they relate to the border. A lot of the tabs are very similar in shape and size, so quite often both parties make errors in fitting pieces together. Each trumpets the other's errors as evidence that the other is all wrong, and even spends some time trying to take apart the other's assembled pieces. The advance of science has now built the puzzle to the point that religion has had to realize that many of their pieces are from a different puzzle altogether, but I suspect we're just reaching the point where some of the pieces that religion has assembled are going to match up with what science has assembled. No one, of course, has access to the picture on the box. It's probably kittens with string.

Whee, that was so much fun I never got to the story. Next time. Oh and Canadians, don't think about it too long: your 2008 taxes have to be filed by midnight tonight.

TAS - HW != GS

A couple of days ago I posed this puzzle:

Here is a wind speed puzzle. Your course is due north, 000 degrees. That is you will proceed in a straight line over the ground to a point that is due north of where you are now. The wind is blowing from 100 degrees, that is from mostly off your right wing, but slightly behind you. With no wind at all, your groundspeed would be 100 knots. Will your groundspeed in the described conditions be greater than, less than or equal to 100 kts?

Some who posted was smart enough to know that the answer is, "it depends on the windspeed." That may seem strange when all I asked for was the sign of the change in speed, but it's true.

As a general rule of thumb, if the wind is blowing from ahead of you, it slows you down, and if it is blowing from behind you it speeds you up, just as you'd probably expect. In rough flight planning I estimate that an n knot wind from m degrees behind me resolves into nSIN(m) worth of tailwind and then add the tailwind to the true airspeed to get groundspeed. (Don't think I'm some kind of walking trig table: when I say I estimate the sine of an angle we're talking "negligible," "a bit," "a lot," "half," "most," and "all.") But when the crosswind component represents a significant proportion of the speed of the airplane, things become more complex.

When there is a significant crosswind, the airplane heading is noticeably not the same as the course. The airplane travels diagonally over the ground with respect to the direction it is pointing. This means that some of the thrust of the airplane is being used to keep the airplane from being blown off course. Logically, then, that reduces the thrust available to maintain groundspeed along the track. So the component of the wind along the track is increasing the groundspeed of the airplane, but the crab is simultaneously decreasing the groundspeed.

If you haven't got your own flight computer handy, try this online one. Scroll down to the third section: Heading, Ground Speed, And Wind Correction Angle. Put in a wind direction of 100, a true airspeed of 100 and a course of 0. Now enter a wind speed of 20 and press Calculate. The calculated groundspeed is 102, so that's two knots of tailwind. Try it again with 37 knots of wind, for a calculated groundspeed of 100. Try it again with sixty fricking knots of wind, like I had the other night, and you calculate a groundspeed of 91 kts. Yeah, the wind is behind you, and you're still down nine knots.

For a given wind speed and direction the amount of head or tailwind is fixed, but the crab angle and thus the proportional reduction in speed due to the crosswind is related to the ratio between the true airspeed of the airplane and the strength of the wind. So the same wind could provide an increase in speed for a fast airplane and a decrease in speed for a slow airplane going the same direction at the same altitude. Bizarre, eh?

My favourite answer was provided by Paul, who amusingly pointed out that all your calculations will be in vain because ATC will vector you into the wind no matter what.

It's disorienting enough flying in the dark in turbulence with a whopping big wind correction angle, but when I found that I needed to fly at a high power to maintain a groundspeed of 140 whether I was going north or south it just felt unfair. You get cheated in wind anyway, because the time lost being slowed down by a headwind is not regained flying the same distance with the same wind on the tail. But when you're slowed down by wind going both ways. Well I want to complain.

The controller working Houston Center was being funny, telling every pilot who checked in that he had "reports of intermittent chop at all flight levels, so just tell me what altitude you want to be bumpy at." Around ten in the evening airline movements diminish and the frequency quiets. I called up Houston and told him I'd like to complain about the sixty knot winds. "Okay," he said, "But I'm not going to do anything about it." As I told him: yeah, I knew. It just makes me feel better to complain.

Does the fact that I'm amused that the sign of the change depends on the sine of the wind direction a sign that I'm a word geek or a math geek? Signed, Aviatrix.

P.S. The bruise is lots of pretty colours, but it's just a bruise, nothing to worry about.

Segmented Weights

When I blogged about how to calculate the loaded weight of an airplane, lots of folks pitched in with other related issues, like how much a planeload of passengers really weigh. At my current job, I work with the same people for weeks at a time, and if I'm going to pick up someone new, the people I'm with can tell me, often with mirthful laughter, how much I should allow for the weight of their colleagues. So I always use actual weights or my own best estimates based on looking at people and lifting cargo.

I linked already to the recently revised Canadian standard weights for males, females, children and infants, and reader Christopher linked to a Transport Canada document proposing new changes to weight and balance practices for small airplanes.

The report describes the limitations of applying standard weights to small aircraft weight and balance calculations.

Companies will naturally try to maximize the load to optimize the service and remain competitive with other companies. This means that, on any given day, many flights operate at close to maximum gross weight on paper when, in fact, some of these flights are operating above maximum gross weight.

Statistical probability dictates that the smaller the sample size, the more the average of the sample will deviate from the average of the larger universe. Because of this, the use of standard average passenger weights when transporting 9 or less passengers does not provide an acceptable level of confidence for ensuring compliance with aircraft weight limitations.

The TC document points out that the law requires the operator to ensure not that the airplane is within limits on paper, but that No person shall operate an aircraft unless, during every phase of the flight, the load restrictions, weight and centre of gravity of the aircraft conform to the limitations specified in the aircraft flight manual. It suggests two solutions, using actual passenger weights and something called segmented weights.

The situation it describes is absolutely true. Pilots do the weight and balance according to standard passenger weights and not according to the size of the actual passengers. When you fly a charter in an eight-passenger airplane, you're generally flying a group of related people. People in a family share eating habits and genetics, so if one is heavy, you typically have a group of eight heavy people. The northern diet is heavy on pop and potato chips, and thus the northern resident is heavier than the average Canadian.

Using actual passenger weights is already an option, and some operators already use it. Northern passengers put up with all kinds of indignities, and I didn't see anything to indicate that the culture of thinness was ingrained to the point that people would be grievously offended by a weigh in before boarding. One problem is that the passengers don't usually show up in time for the pilot to do the calculations between when they arrive and when they board. A smart pilot precalculates the weight and balance for the whole day, before she sees a single passenger. So what is this segmented weights, thing? I've never heard of it before. It looks like statistics. I have some mathematics training including one pathetically easy statistics course, so I should be able to figure this out.

It's like I'm returning to the original purpose of the blog: learning things!

This concept involves adding a portion of the standard deviation to an average weight in order to increase the confidence that the actual weight of a passenger and carry-on baggage will not exceed the resultant, increased weight value called segmented weight.

For a large sample, like two hundred people on a large jet, chances are good that the pounds carried on board by people who weigh more than population average will be balanced by pounds not carried on by people who weigh under that average. But as the number of people boarding decreases, so does the probability that their average will be significantly different than the population average. So as the number of people boarding decreases, you need to add a fudge factor to hedge against the possibility of having a load of biggies throw off your W&B. As the seating capacity goes down, the fudge factor per passenger goes up.

People with more statistics training than I have have worked out a table and state that if I use the row appropriate to the seating capacity of my airplane and the column appropriate to the male/female ratio, I will have a "95-percent confidence level and a 1-percent tolerable error." That apparently means "good enough for the government." This all assumes that the current standard passenger weights do accurately reflect the overall average weight of that portion of the public who travel on airplanes, weighted by their frequency of travel.

The chart has a bit of a problem for someone doing row-by-row seating. Lets say I have an eight passenger airplane, full in the summer, with two guys in the back, a man and a woman in the next row, two women in the next and two guys up front. That's five guys and three women, a 62/38 M/F split, so I guess I'll use the 60/40 column. Therefore according to the Canadian summer chart, I count my eight people at 215 each, for a total passenger weight of 1720 lbs. That works fine for the weight, but how am I supposed to do the row-by-row balance? My best guess is that I should use the figure of 192 lbs for the women and 231 lbs for the men, because those are the figures I'd use per passenger if the load were all female or all male respectively. That would give me a total of 1731 lbs in the final W&B. So can I put on that extra eleven pounds of fuel or not?

Okay, maybe it's because I rounded the 62% to 60%. If the load were half men and half women, the average would be 211, for a total weight of 1688. Four women at 192 lbs plus four men at 231 lbs adds up to 1692. That's only four pounds off, but what is the pilot supposed to do with those four extra pounds in the paperwork? You have to do the math row by row, because you may have to swap men and women back to front to get the CofG to work out.

I don't think these new weights will change the amount of weight on a typical charter flight. If the pilot would have flown with the load under the old rules but it comes out as overweight using the new rules, the pilot will either take fuel out of the paperwork, but not out of the plane; or they'll officially use "actual weights" and pilots can be really bad carnival weight guessers.

Meanwhile examining the tables closely tells me some interesting things. We're told that Transport Canada allowed eight pounds for summer clothing in determining passenger weights from the health survey weights, but they advise pilots to add ten pounds to volunteered weights. That means that Transport Canada assumes the average Canadian passenger lies about his or her weight by taking off two pounds.

Comparing the FAA and Transport Canada tables, we see heavier passenger weights in the former table in each category. I thought the difference might be carry-on rules but they actually mask a greater difference, because the American table includes only six pounds per person for carry-on baggage while the Canadian table includes thirteen pounds of carry-on bags per passenger. Both tables are recently updated. It's not a clothing difference either, because I'm comparing summer weight to summer weight. Canadians add six pounds for winter and Americans add five. Conclusion: Americans weigh more than Canadians, but Canadians have heavier parkas and boots.

Also: airplane missing in the Bermuda Triangle.

Tailwind (Part II)

A while ago I posted a picture of my airspeed indicator and my GPS and asked you to calculate my tailwind. It's slightly harder than it looks, and you were missing a couple of pieces of information required for the complete calculation.

The airspeed indicator is showing 149 kts and the GPS 223 kts, so if you assume that the former is how fast the airplane is moving through the air and the latter is how fast the airplane is moving over the ground, it would seem completely reasonable to subtract them to determine how fast the air is moving over the ground. And that's how you arrived at your first collective guess of 74 kts.

The problem with that argument is that the airspeed indicator is calibrated to show true airspeed only at sea level and standard conditions. At higher altitudes or significantly non-standard temperatures, it needs to be adjusted to get the true airspeed, i.e. the speed the airplane would be going over the ground in zero wind. The true air speed increases with respect to the indicated airspeed by about two percent per thousand feet above sea level. I see from the GPS that I'm flying at about 9500' asl, so an in-the-head calculation has the true airspeed about 19% higher than the indicated, or 178 kts. That would suggest a tailwind of 223 minus 178, which equals 45 kts.

That is pretty rough, and assumes standard conditions. To get more precise than the two percent rule-of-thumb, you'd need to know the calibrated airspeed, the outside air temperature and the pressure altitude.

I didn't give you--and indeed didn't record--the outside air temperature but I think I had mentioned temperatures around freezing: raining some days and snowing others, and that a warm front was approaching, so you wouldn't be wrong to guess that after the arrival of that warm air mass there might be surface temperatures below standard but above freezing, around 5 to 10 degrees C. The temperature can be expected to drop off about 2 degrees per thousand feet of altitude, so at 9500' it might have been -5 to -10, and I recall -10 being about what I saw on the OAT gauge.

You know I was VFR on this trip: I think I mentioned the holes in the dashboard where some of my IFR instruments ought to be, and you see that the bearing is southeast. Therefore, according to what in Canada are still known as the cruising altitude orders I should have been at an indicated odd thousand foot altitude plus 500'. The GPS shows me at 9359', so that confirms that I was flying at an indicated 9500'. The difference between GPS altitude and indicated wouldn't be 2000' at these temperatures over prairie. (In very cold temperatures with mountain wave effect the GPS altitude could be 3000' lower than indicated). The difference between indicated altitude and pressure altitude depends on the altimeter setting, but I already sent my operational flight plan from that leg into company for filing, so I don't have the recorded altimeter setting to calculate from. We'll assume standard pressure, so that pressure altitude would be the same as indicated. It wasn't far off.

Calibrated airspeed corrects indicated airspeed for position error, but in cruise this difference is negligible, so I'll stick with 149 kts as the CAS.

I then use an E6B flight computer to crunch the numbers. I don't have one with me as I type, so I used a simulator from the web. Punch in 149 kts, -10C, and 9500' and I get 168 kts TAS. And 223 minus 168 equals 55 kts.

There's actually a calculator built right into this particular airspeed indicator, as someone pointed out, but the photograph is not clear enough to show it. (The reader who zoomed in and read the TAS there anyway may have seen it correctly, but I hadn't set that calculator, so its indications were meaningless). If I had used it, I would have set the pressure altitude opposite the outside air temperature at the top, then the needle that shows 149 kts on the main scale would also be pointing to a value on the white, outer scale, which would be the true airspeed. I'll try to get a better photograph of it sometime.

This is the reverse of the calculation one does to determine how long it will take to reach destination given a particular wind. But most of us cheat and use computer programs that do that for us now.

Tailwind

I took some pictures on the way south, although as usual the instrument shots didn't work out well. I'll leave it as an exercise for you to calculate how much tailwind I had.

It's the sort of thing you can do in flight to keep your mind awake.

The Balance Part of W&B

As well as not asking the airplane wings to lift more weight then the manufacturer intended, you need to make sure that the front-to-back balance of the weight is acceptable. To do this you take into consideration the weight of each component of the load, and the location at which it is loaded.

Weight, Arm and Reference Datum

Consider a teeter-totter (or a see-saw, whatever you call that spinal injury-inducing levered plaything in your neck of the woods). If you weren't denied the opportunity to have played on one, you know that if you put an adult (or two kids) at one end and one kid at the other, it's hard for those on the heavy end to push off the ground, and easy to launch the kid into orbit if the adult lets his end come down hard. For easy teeter-tottering, you have to pile up more kids at the light end, or have mom sit closer to the fulcrum (the hinge supporting the see-saw) where her weight has less leverage. The effect of someone sitting on the teeter-totter is directly proportional to how much she weighs, and to how far she is from the middle. If Mom weighs twice as much as Junior she has to sit halfway between the end and the middle to balance Junior at the other end. Mathematically put, the teeter-totter balances when Mom's weight times her distance from the middle equals Junior's weight times his distance from the middle.

The distance out is called arm and the combined effect of weight and distance, the weight times the arm, is called moment. As Mom's moment (say 60 kg x 2 m) tends to push the see-saw one way and Junior's (30 kg x 4 m) pushes it the other way, and they are equal, they balance. I can also call Mom's arm (distance to the right) positive and Junior's arm (to the left) negative, so that the total moment of the system becomes (60 x 2) + (30 x -4) = 0. A total moment of zero means no moment, so no tendency to move about the fulcrum and the see-saw balances. Whee. (I'm ignoring the weight of the teeter-totter itself, because presumably it's balanced). If Mom sits all the way out to her end, her arm increases to 4 (further to the right), so the total moment becomes (60 X 4) + (30 x -4) = 120. That 120 is a measure of the unbalancedness. [Physicists: please don't beat me up for using kilograms instead of newtons for weights here, and then ignoring dimensions. I know the difference. I just don't feel anything is added to the explanation by multiplying both sides of the equation by g.] The point I measure from is called the reference datum, and its position is irrelevant, as long as everything is measured from the same place.

Here is an example to explain that last italicized phrase. I postulated an eight metre teeter-totter, and the measurements I gave were from the middle. That wasn't too hard, as the middle is easy to find, but it did require the measurements in one direction to be negative, with some people find inconvenient. We could take the same teeter-totter and measure from one end, say Mom's end. So Mom's moment, when she is halfway to the middle in order to balance Junior, becomes (60 x 2 = 120) and Junior's becomes (30 x 8 = 240), for a total moment of 360. If we put Mom back at the end now, her arm would be zero, so the total moment would be (0 x 60) + (30 x 8) = 240. Notice that 360 (the ideal) minus 240 (the moment with Mom at the end) is 120. The unbalancedness is still 120. I could even measure from the swingset or from the edge of the playground and get the same result.

Centre of Gravity

When the reference datum is an arbitrary point, the moment, the measurement of unbalancedness, is an arbitrary number, and these numbers get quite large when you're dealing with long, heavy airplanes. So we put it all together to get a non-arbitrary number called the centre of gravity. Weight multiplied by arm equals moment not only for each component of the system, but also for the sum of all its components. And if weight times arm equals moment, then moment divided by weight equals arm. Back to the total weight and moment of the unbalanced teeter-totter.

Mom and Junior together make 90 kg, so that's the weight. And I already totalled the moments for each reference datum.

Measuring from the middle: 120 / 90 = 1.33

Measuring from the end: 240 / 90 = 2.67

Now, measuring 1.33 m from the middle towards Mom's end reaches the same point as measuring 2.67 m from Mom's end toward the middle. That is the point at which the teeter-totter would balance with Mom at one end and Junior at the other. That's still called the arm of the loaded airplane, but more commonly called the centre of gravity, often written CofG and pronounced see-uhv-gee.

Example

For the airplane, every manufacturer defines a reference datum, and publishes a list of the arms of every point at which weight will be loaded, such as each fuel tank, the pilot seat, each row of passenger seating, and each baggage area. The manufacturer also publishes a chart showing the acceptable range of moment and or centre of gravity (CofG). It's the pilot's job to calculate the total moment or CofG of the loaded airplane and ensure that it falls within the limits of the chart.

Here's an example, from a Piper Seneca. It's a fairly simple airplane, and I've simplified it further by not using one of the baggage areas. Note that this calculation applies to a particular Piper Seneca, one that once belonged to the Winnipeg Flying Club. A different Piper Seneca would have a different empty weight and arm.

We'll imagine a 200 lb pilot, 460 pounds of passengers, in two different rows, and 50 lbs of baggage in the back. The first line of the table I read off the individual airplane weight and balance document. The other weights I get from inspection. The other arms are from the Aircraft Flight Manual, based on a reference datum near the nose of the airplane. The moments are the product of the weights and arms. The total weight and total moment are simply a sum of the individual weights and moments. And the total CofG is the total moment, divided by the total weight.

	Weight	Arm	Moment
Airplane	2944	85.82	252674
Fuel	550	93.6	51480
Pilot	200	85.5	17100
Pax1	160	118.1	18896
Pax2	300	155.7	46710
Baggage	50	178.7	8935
----------	-------	----------	---------
Total	4204	94.1	395795

The total weight of 4204 happens to be four pounds over the maximum weight allowed by the manufacturer, while the CofG is just forward of the maximum 94.6. In this case I would accept the load, because I know I will burn about eight pounds of fuel during taxi, runup and on the takeoff roll. By the time the airplane takes to the air, it will be within limits. The manufacturer tells me that the effect of fuel burn on CofG for this airplane is negligible.

It bears noting that this airplane has an additional baggage area in the nose, and two unoccupied seats. Three medium-weight passengers and their carry-ons is enough to load the airplane to its maximum. An airplane doesn't have to be stuffed to be full.

If the CofG numbers get unwieldy, there's another way to express them. I'll tell you about %MAC calculations some other time. And this isn't one of my best explanations, so ask away if I've said anything confusing.

Weight Calculations

This is the first of a two-part post on calculating weight and balance of a loaded aircraft, as eighty percent of private pilots are purported not to know how to do. I promised a while ago to explain, and it turns out that a post a few days hence requires some understanding of the subject, so now is the perfect time. Today I'll look at weight, the easy part. Tomorrow's post will look at balance, which really isn't all that complicated. I just got carried away and wrote too much to swallow in one bite.

Aircraft have published maximum weights. There may be a separate maximum ramp weight (how much the loaded airplane may weigh just to sit there on its wheels and taxi around), maximum take-off weight (what it says), maximum zero fuel weight (effectively requiring a certain proportion of the weight to be in the fuel tanks, bending the wings down, as opposed to being in the fuselage, where it bends the wings up), and maximum landing weight (what it says). Depending on the type of operation, those weights may change depending on the temperature and available runway. For safe, legal flight the airplane must be under each of these weight requirements for the appropriate stage of flight.

To find the total weight, you must know the weights of the various components. One of the documents belonging to an individual airplane will state how much the airplane alone weighs. Yep, someone had to weigh it. When they add or change equipment they don't have to re-weigh it, though. They can just do the math. So if you take out a basic 20 lb seat and replace it with a deluxe 35 pound seat, you increase the basic empty weight by fifteen pounds. The BEW includes the airplane, the engines, the seats, the avionics, everything that is installed in the airplane and also full hydraulic fluid and the like. It usually includes full oil but there are exceptions, so you need to examine your paperwork carefully. It even includes what's called the unusable fuel: the fuel that could be left sloshing around in the bottom of the tanks if you were to run the engine until it stopped from fuel starvation, in some reasonable flight attitude. You read the empty weight of the airplane off the weight and balance (W&B) document, make any adjustments written in the journey log, and write down that number.

A commercial airplane may be dispatched with a Standard Operating Weight, which is the basic empty weight of the airplane plus the weight of the crew and their personal equipment. Sometimes the SOW is calculated and written in the journey log book as if the crew are both males, so that when one of more of the crew is female, the weight can be adjusted, to carry an extra thirty pounds of fuel. If the airplane doesn't list a standard operating weight, the crew and their gear are counted along with the passengers. It doesn't matter which way, so long as it adds up, and complies with what the regulatory authorities have approved if it's a commercial operation.

Next you add fuel. The usable fuel is the fuel the manufacturer says is available for your use in all normal flight attitudes. Avgas weighs six pounds per U.S. gallon and jet fuel weighs about seven. These weights vary with the temperature and exact grade, and you can use a table to work out the weight for the volume of fuel you will have in the tanks. (The numbers I'm quoting are in American units because the airplanes I fly were built in the US and so the operating manual lists weights and fuel volumes that way. If you buy a new Airbus (or even Boeing for delivery outside the US) I'm sure you can get the documentation in kilograms and litres.

The remaining weight on board will be cargo and passengers. Cargo is weighed, as you know from checking baggage at the airport. Some charter operations have a big floor scale and simply ask all the passengers to stand on it with their cargo. "You're 200 lbs over," the boss says. It's up to the customer to decide whom or what to leave behind. In a remote charter operation, the pilot may estimate and mentally sum the weights of articles loaded. I've also done it by standing on a bathroom scale as I lifted each bag and subtracting my weight from each reading in order to add up the total weight on board. Some pilots carry a handheld spring-based scale, which works if every article has a handle or other point that the scale can hook onto. You lift the scale with the hook holding the item, and extension of the spring moves a pointer indicating the weight of the item.

Passengers are rarely physically weighed but may be asked for their weights, estimated by the pilot or dispatcher, or counted at standard weights, depending on the operation. In Canada, standard weights count clothed females at 165 lbs and males at 200 lbs each. Everyone is assumed to weigh six pounds more in the winter, and the weights include a 13 lb carry on. A charter operator that weighs all baggage as cargo, and thus has no uncounted carryons can count men at 187 lbs, but a pilot flying a charter for the Toronto Argonauts football team is expected to apply reasonable weights for football players, not just use the defaults.

Once numbers for the airplane, people, bags and fuel have been obtained, you just add them up. If the total is over the maximum then you can load less fuel (but not less than the legal minimum), or leave passengers or cargo behind. Once the weight is within limits, so far so good, but you must make sure that the airplane will also be loaded within balance limits. That's tomorrow's posting. Because, as I mentioned, I got carried away.